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Light Wave Vs. Particles Wave Vs. Particles Electromagnetic Electromagnetic Waves Waves Frequency and Wavelength Frequency and Wavelength Michelson-Morely Experiment Michelson-Morely Experiment Light Vs. Sound Light Vs. Sound Space Travel & The Speed of Space Travel & The Speed of Light Light Why Objects Have Color Why Objects Have Color Primary and Secondary Colors Primary and Secondary Colors Light Colors Vs. Pigments Light Colors Vs. Pigments The Electromagnetic Spectrum The Electromagnetic Spectrum Parallax and Depth Perception Parallax and Depth Perception Light Transmission Light Transmission Thin Films & Thin Films Thin Films & Thin Films Interference Interference Luminosity Luminosity Polarized Light Polarized Light Planck Planck s Constant s Constant Coherent Light Coherent Light Lasers Lasers Holograms Holograms Luminous Flux Luminous Flux Illuminance Illuminance Luminous Intensity Luminous Intensity Luminous Flux vs. Power Luminous Flux vs. Power Luminous vs. Illuminated Luminous vs. Illuminated

Light Wave Vs. Particles Wave Vs. Particles Electromagnetic Waves Electromagnetic Waves Frequency and Wavelength Frequency and Wavelength Michelson-Morely

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Light

•Wave Vs. ParticlesWave Vs. Particles•ElectromagneticElectromagnetic WavesWaves•Frequency and Frequency and WavelengthWavelength•Michelson-Morely Michelson-Morely ExperimentExperiment•Light Vs. SoundLight Vs. Sound•Space Travel & The Space Travel & The Speed of Speed of Light Light•Why Objects Have ColorWhy Objects Have Color•Primary and Secondary Primary and Secondary ColorsColors•Light Colors Vs. Light Colors Vs. PigmentsPigments•The Electromagnetic The Electromagnetic SpectrumSpectrum•Parallax and Depth Parallax and Depth PerceptionPerception

•Light TransmissionLight Transmission•Thin Films & Thin Films Thin Films & Thin Films

Interference Interference•LuminosityLuminosity•Polarized LightPolarized Light•PlanckPlanck’’s Constants Constant•Coherent LightCoherent Light•LasersLasers•HologramsHolograms•Luminous FluxLuminous Flux•IlluminanceIlluminance•Luminous IntensityLuminous Intensity•Luminous Flux vs. PowerLuminous Flux vs. Power•Luminous vs. Luminous vs. IlluminatedIlluminated

Light: Introduction

Isaac Isaac NewtonNewton

Robert Robert HookeHooke

Christian Christian HuygensHuygens

For centuries the nature of light was For centuries the nature of light was disputed. In the 17th century, Isaac Newton disputed. In the 17th century, Isaac Newton proposed the proposed the ““corpuscular theorycorpuscular theory”” stating stating that light is composed of particles. Other that light is composed of particles. Other scientists, like Robert Hooke and Christian scientists, like Robert Hooke and Christian Huygens, believed light to be a wave. Today Huygens, believed light to be a wave. Today we know that we know that light behaves as both a wave light behaves as both a wave and as a particleand as a particle. Light undergoes . Light undergoes interference and diffraction, as all waves interference and diffraction, as all waves do, but whenever light is emitted, it is do, but whenever light is emitted, it is always done so in discreet of packets called always done so in discreet of packets called photons. These photons carry momentum, but photons. These photons carry momentum, but not mass.not mass.

Wave Vs. Particles

If light did need a medium If light did need a medium in order to propagate, the in order to propagate, the earth would spend its days earth would spend its days submerged in darkness and submerged in darkness and the sun would not be the sun would not be visible.visible.

Light is an electromagnetic wave. As light Light is an electromagnetic wave. As light travels through space an electric field and a travels through space an electric field and a magnetic field oscillate perpendicular to the magnetic field oscillate perpendicular to the wave direction and perpendicular to each other. wave direction and perpendicular to each other. We We’’ll learn more about these fields in later ll learn more about these fields in later units. A light wave is transverse rather than units. A light wave is transverse rather than longitudinal, since each field oscillates in a longitudinal, since each field oscillates in a plane perpendicular to the direction of the plane perpendicular to the direction of the wave. Unlike a pulse traveling down a length wave. Unlike a pulse traveling down a length of rope, nothing is physically moving in a of rope, nothing is physically moving in a light wave. Light requires no medium! It can light wave. Light requires no medium! It can travel through space that contains matter (such travel through space that contains matter (such as air, glass, or water) or through a vacuum.as air, glass, or water) or through a vacuum.

Electromagnetic Waves

Above is a set of 3-D coordinate axes. Above is a set of 3-D coordinate axes. The The zz -axis is vertical, the y-axis is -axis is vertical, the y-axis is horizontal, and the horizontal, and the xx -axis is coming -axis is coming out toward you.out toward you.

Electric and magnetic fields affect charges. Electric and magnetic fields affect charges. Light is an electric field coupled with a Light is an electric field coupled with a magnetic field. The two fields oscillate magnetic field. The two fields oscillate together but in different planes. To together but in different planes. To visualize an electromagnetic wave, you must visualize an electromagnetic wave, you must think in 3-D. Letthink in 3-D. Let’’s put a light wave s put a light wave together one piece at a time. together one piece at a time.

Electromagnetic Waves (cont.)

The red wave represents an oscillating The red wave represents an oscillating electric field in theelectric field in the y-zy-z plane. (Every plane. (Every point on this curve has an point on this curve has an xx coordinate of coordinate of zero.) It is a snapshot in time. At the zero.) It is a snapshot in time. At the crests and troughs, the electric field crests and troughs, the electric field will exert the greatest force on a charge, will exert the greatest force on a charge, but in opposite directions. Charges but in opposite directions. Charges located at the located at the yy -intercepts will -intercepts will experience no electric force (at this experience no electric force (at this point in time). point in time).

Electromagnetic Waves (cont.)

Bottom right is shown an Bottom right is shown an electric and a magnetic electric and a magnetic field oscillating field oscillating together. This is an together. This is an electro-magnetic wave electro-magnetic wave (light). The fields (light). The fields travel through space travel through space together. They have the together. They have the same period and same period and wavelength, but they wavelength, but they oscillate in two different oscillate in two different planes, which are planes, which are perpendicular to each perpendicular to each other. The electric other. The electric field, the magnetic field, field, the magnetic field, and the wave direction are and the wave direction are all mutually all mutually perpendicular. For some perpendicular. For some additional pictures, check additional pictures, check out these links below. out these links below. Remember, what youRemember, what you’’re re seeing is just a snapshot seeing is just a snapshot in time (see animation). in time (see animation).

Wave Pic Light animation

Propagation in matter

Oscillating charge animation

In the top right picture, the blue wave represents an In the top right picture, the blue wave represents an oscillating magnetic field in the oscillating magnetic field in the x-yx-y plane. (Every plane. (Every point on this curve has an point on this curve has an zz coordinate of zero.) It is coordinate of zero.) It is a snapshot in time. Like the electric field, the a snapshot in time. Like the electric field, the magnetic field is strongest at the crests and troughs. magnetic field is strongest at the crests and troughs.

Frequency and Wavelength

Light Sound

Frequency Color Pitch

Amplitude Brightness Loudness

The frequency of a light wave corresponds to the The frequency of a light wave corresponds to the color we see. The amplitude corresponds to color we see. The amplitude corresponds to brightness.brightness.

The frequency of visible light is extremely high The frequency of visible light is extremely high compared to that of audible sound. Red light, for compared to that of audible sound. Red light, for example, is the lowest frequency of visible light, example, is the lowest frequency of visible light, but even red light has a frequency of over 400 but even red light has a frequency of over 400 trillion Hertz. This means if youtrillion Hertz. This means if you’’re looking at a re looking at a red light, over 400 trillion full cycles of red red light, over 400 trillion full cycles of red light enter your eye every second! The frequency light enter your eye every second! The frequency of violet light is even higher—over 750 trillion of violet light is even higher—over 750 trillion Hz. Other types of electromagnetic radiation, Hz. Other types of electromagnetic radiation, like X-rays, have even higher frequencies, and like X-rays, have even higher frequencies, and some have lower frequencies, like radio waves. some have lower frequencies, like radio waves. Just as our ears are only capable of hearing Just as our ears are only capable of hearing certain range of sounds (20 – 20,000 Hz), our eyes certain range of sounds (20 – 20,000 Hz), our eyes can only see a small range of frequencies.can only see a small range of frequencies.

Frequency and Wavelength (cont.)

High Frequency ↔ Small Wavelength

Low Frequency ↔ Long Wavelength

Vacuum speed is constant.

Because visible light waves have such high Because visible light waves have such high frequencies, their wave-lengths are very short. frequencies, their wave-lengths are very short. Recall the formula Recall the formula v = v = ff (wave speed = (wave speed = wavelength wavelength frequency). Since light of any frequency). Since light of any frequency always travels at the same speed in a frequency always travels at the same speed in a vacuum, vacuum, vv is a constant. Thus, the biggeris a constant. Thus, the bigger ff is, is, the smallerthe smaller must be. Red light, for example, must be. Red light, for example, has a wavelength of only about 700has a wavelength of only about 700 nm. (1nm. (1 nm = 1 nm = 1 nanometer = 10nanometer = 10-9-9 m = 1 billionth of a meter.) m = 1 billionth of a meter.) Violet light has an even smaller wavelength, since Violet light has an even smaller wavelength, since its frequency is higher. X-rays have still its frequency is higher. X-rays have still smaller wavelengths. Radio waves can have very smaller wavelengths. Radio waves can have very long wavelengths (many meters) since their long wavelengths (many meters) since their frequencies are so low. frequencies are so low.

Historical Background• Before GalileoBefore Galileo’’s time (around 1600), many s time (around 1600), many people believe that light was infinitely fast. people believe that light was infinitely fast. ItIt’’s so fast that it seemed like it took no time s so fast that it seemed like it took no time to get from one place to another. Galileo and an to get from one place to another. Galileo and an assistant went to the Italian countryside, a mile assistant went to the Italian countryside, a mile apart, and tried to measure the speed of light by apart, and tried to measure the speed of light by timing it. All they could determine was that timing it. All they could determine was that light is much faster than sound.light is much faster than sound.• Later that century (around 1667) a Danish Later that century (around 1667) a Danish astronomer named Ole Roemer made the first astronomer named Ole Roemer made the first accurate measurement of the speed of light. He accurate measurement of the speed of light. He had been observing one of Jupiterhad been observing one of Jupiter’’s moons, Io s moons, Io (which Galileo had discovered). As Io circled (which Galileo had discovered). As Io circled Jupiter, it would be eclipsed by Jupiter Jupiter, it would be eclipsed by Jupiter periodically. That is, Jupiter would block Ioperiodically. That is, Jupiter would block Io’’s s view from Earth at regular intervals. Each time view from Earth at regular intervals. Each time Io orbited Jupiter, an eclipse would occur. The Io orbited Jupiter, an eclipse would occur. The time between the eclipses was the period of Iotime between the eclipses was the period of Io’’s s orbit. Roemer noticed that the eclipses orbit. Roemer noticed that the eclipses sometimes took a little longer, and sometimes sometimes took a little longer, and sometimes they took a little less time. Iothey took a little less time. Io’’s period seemed s period seemed to fluctuate: first Io would be behind schedule; to fluctuate: first Io would be behind schedule; then it would be ahead of schedule. This pattern then it would be ahead of schedule. This pattern repeated itself every year, which hinted to repeated itself every year, which hinted to Roemer that the fluctuation had to do with EarthRoemer that the fluctuation had to do with Earth’’s s motion around the sun.motion around the sun.

Historical Background (cont.)

Because Jupiter is farther from the sun, it moves Because Jupiter is farther from the sun, it moves much slower around the sun (recall Keplermuch slower around the sun (recall Kepler’’s third s third law). During the six-month period depicted above, law). During the six-month period depicted above, Earth is moving away from Jupiter. Therefore, the Earth is moving away from Jupiter. Therefore, the light carrying the information of the eclipse took light carrying the information of the eclipse took a little longer to reach Earth, since Earth was a little longer to reach Earth, since Earth was ““running awayrunning away”” from that light. At the end of the from that light. At the end of the six months, the light from Io had to travel an six months, the light from Io had to travel an extra distance about equal to the diameter of extra distance about equal to the diameter of EarthEarth’’s orbit. Roemers orbit. Roemer’’s observed that Io eclipses s observed that Io eclipses were about 8 minutes behind schedule after six were about 8 minutes behind schedule after six months. Knowing approximately Earthmonths. Knowing approximately Earth’’s orbital s orbital diameter, Roemer calculated the speed of light at diameter, Roemer calculated the speed of light at around 125,000 miles per second! Roemeraround 125,000 miles per second! Roemer’’s speed, as s speed, as great as it was, was actually an underestimate. great as it was, was actually an underestimate. The true speed of light is just a half a smidgeon The true speed of light is just a half a smidgeon under 3 · 10under 3 · 1088 m/s, which is about 186,300 miles per m/s, which is about 186,300 miles per second! We call this speedsecond! We call this speed cc. . cc = 2.9979 = 2.9979 101088 m/s m/s 3 3 101088 m/s m/s

Historical Background (cont.)

• RoemerRoemer’’s main contribution was proving that the s main contribution was proving that the speed of light is finite. Since Roemer, several speed of light is finite. Since Roemer, several people contributed to determining the precise value people contributed to determining the precise value forfor cc. In 1849 Louis Fizeau found an excellent . In 1849 Louis Fizeau found an excellent approximation forapproximation for c c without resorting to without resorting to astronomical means. He used a rapidly rotating, astronomical means. He used a rapidly rotating, toothed wheel. He shined a beam of light through one toothed wheel. He shined a beam of light through one opening between the teeth, which reflected off a opening between the teeth, which reflected off a mirror over 5 miles away. When the wheel spun fairly mirror over 5 miles away. When the wheel spun fairly slowly, the light could easily pass through the slowly, the light could easily pass through the opening, reflect, and pass through it again in the opening, reflect, and pass through it again in the other direction before its path was blocked by the other direction before its path was blocked by the next tooth of the wheel. By making the wheel spin next tooth of the wheel. By making the wheel spin faster and faster until the reflected beam of light faster and faster until the reflected beam of light was blocked, Fizeau was able to calculatewas blocked, Fizeau was able to calculate cc. .

• Jean-Bernard Foucault also made accurate Jean-Bernard Foucault also made accurate measurements of measurements of c. c. He shined light at a rotating He shined light at a rotating mirror, which reflected to a stationary mirror, back mirror, which reflected to a stationary mirror, back to the rotating mirror, and finally back toward the to the rotating mirror, and finally back toward the source. Because the rotating mirror turned slightly source. Because the rotating mirror turned slightly while the light was traveling to the stationary while the light was traveling to the stationary mirror and back, the rotating mirror reflected the mirror and back, the rotating mirror reflected the light at a slight angle. This angle allowed him to light at a slight angle. This angle allowed him to calculatecalculate cc..

Michelson-Morely Experiment Albert Michelson is best known for an experiment he did with Edward Morely in 1887. At the time it wasn’t understood that light needed no medium through which to travel. It was proposed that light traveled through an invisible “ether” in space. The Michelson-Morely experiment was an attempt to detect Earth’s motion through the ether. Here’s how it worked: First imagine you’re standing still outside and there is a wind coming from the north. If you run north, you’ll measure a greater wind speed. If you run south, you’ll measure it slower. Whether you run north or south, though, you’ll still feel the wind coming from the north. If you run east or west, however, not only will the wind seem to change speed, so will its direction.

Now imagine a race between two equally fast swimmers. They each go the same distance in a river, but one goes upstream and back while the other goes directly across the river and back. With no current the race would definitely be a tie, since their speeds and distances are the same. With a current, however, the cross-stream swimmer will win. This is not obvious. You should try to prove this. For a hint see the “river crossing--relative velocities” slide from the presentation on vectors. It involves the same principle as Michelson’s interferometer (but without lasers).

Michelson-Morely Experiment

Michelson-Morely Experiment (cont.)

Michelson

Einstein

Michelson built something called an interferometer to try to measure a change in the speed of light in two different directions. The Earth moving through the ether around the sun is analogous to a wind or current. Instead of racing two swimmers, Michelson raced beams of light. Light was shone onto a mirror that allowed half of it to pass through. Each beam traveled the same distance before being reflected back and allowed to recombine. Based on the interference pattern of the combined waves, Michelson should have been able to detect a winner. But no matter how the experiment was done, the race was always a tie. This eventually forced physicist to abandon the ether theory. Einstein resolved the problem in 1905 with his theory of special relativity. In it he asserts that the speed of light is the same no matter how fast or which way an observer is moving.

Light Vs. Sound

(Solution on next (Solution on next slide)slide)

It is important to emphasize just how fast light is. Compared to light, sound is a snail. A wise person once said, “Light travels faster than sound, which is why some people appear bright until you hear them speak.” Have you ever watched a baseball game from a distance? You see the batter make contact with the ball, but the sound of the wallop is delayed. This is because, although sound is really fast, light is super-duper fast. For all practical purposes, when you see something is when it happened (at least for events here on Earth). You can determine how far away a lightning strike is by counting seconds from the time you see the lightning until you hear the thunder. It takes sound about 5 s to travel a mile, so if the thunder lags behind the lightning by 2 or 3 s, then the lightning strike occurred about half a mile away.

Problem: You hear a thunder clap 6 s after you see the lightning. Assume the speed of sound to be 343 m/s. How far away is the lightning?

Light Vs. Sound (cont.)

Sound Sound WavesWaves

Light Light WavesWaves

Solution on next Solution on next slide slide

Answer: Ignoring the small amount of time light needs to travel to you, we have:

d = v t = (343 m/s) (6 s) = 2058 m

Problem: Now let’s do the same problem without ignoring light’s travel time:

Light Vs. Sound (cont.)

Answer: Let t = time it takes the light to reach you. In that time the sound of the thunder only travels a short distance. Since you hear the thunder 6 s after you see the lightning, the sound travels for (6 s) + t. The light and sound each travel the same distance, so:

343 (t + 6) = (3 · 108) t t = 6.8600078 · 10-6 s d = 2058.0024 m

So, the lightning strike really occurred a couple millimeters farther away than we had calculated the first way. Note: The difference in results is meaningless here since we can’t know the time delay or the speed of sound to as many significant digits as our answer has.

Space Travel & The Speed of Light

Solution on next slide

We can’t always ignore the time light takes to travel. Whenever you look into the night sky, for example, you’re really looking back into time. The stars you see are so far away that the light they emit takes years to reach us. Nearby stars are tens or hundreds light-years away. A light-year is the distance light travels in one year, almost 6 trillion miles. (Our sun is only about 8 light-minutes away).Problem: Schmedrick is on a space journey heading toward Alpha Centauri, the nearest star excluding the sun, which is about 4.3 light-years away. Schmedrick's rocket goes a constant 0.03 c (3% of the speed of light). As he passes Alpha Centauri he sends a radio message back to Earth and continues traveling away from Earth. The Earthlings reply immediately. How long must Schmedrick wait for his reply?

Space Travel & The Speed of Light (cont.)

A. C.A. C.

SS..

4.3 4.3 lyly

vv tt

Answer: Since we know a trip back and forth from Alpha Centauri takes a total of 8.6 years, we can set up our equation in the following way:d = vt (c = 1 in light years per year)

8.6 + v t = c t 8.6 + 0.03 c t = c t 8.6 + 0.03 t = t 8.6 = 0.97 t 8.6 / 0.97 = 8.87

Schmedrick will have to wait 8.87 years to get a reply back from earth. Links: Find out more about Alpha Centauri here.

Why Objects Have Color

In the first picture the tomato absorbs blue and In the first picture the tomato absorbs blue and green wavelengths and reflects the red wavelength. green wavelengths and reflects the red wavelength. In the second picture red light is shone upon the In the second picture red light is shone upon the tomato. The tomato is still reflecting the red tomato. The tomato is still reflecting the red wavelength and thus still looks red. But in the 3wavelength and thus still looks red. But in the 3rdrd picture blue light is shone upon the tomato, and picture blue light is shone upon the tomato, and since the tomato absorbs the blue wavelength the since the tomato absorbs the blue wavelength the tomato appears to be black.tomato appears to be black.

Links:Links: Prism (light broken down in (light broken down in different wavelengths.different wavelengths.

Visible light is a combination of many wavelengths (colors), which give it a white appearance. When light hits an object certain wavelengths are reflected and others are absorbed. The reflected wavelengths are the ones we see and determine the color of an object.

Primary and Secondary Colors

The primary light colors are Red, Blue, and Green The primary light colors are Red, Blue, and Green (RGB).(RGB).

The secondary light colors are Yellow, Cyan, and The secondary light colors are Yellow, Cyan, and Magenta.Magenta.

Combining pigments in painting is exactly the Combining pigments in painting is exactly the opposite: opposite:

The primary pigments are Yellow, Cyan, Magenta.The primary pigments are Yellow, Cyan, Magenta.

The secondary pigments are Red, Blue and Green.The secondary pigments are Red, Blue and Green.

Animation

Light Colors Vs. PigmentsPrimary colors in light are red, green, and blue because when put together in the right intensities they form white light. Televisions use this idea to project pictures on the screen. When lights these colors are combined in pairs they form the secondary colors for light.

Pigment colors are seen by reflected light. A primary pigment color is one that absorbs only one primary light color and reflects the other two primary colors. Thus yellow, magenta, and cyan are the primary colors for pigments. Yellow reflects red & green, cyan reflects green & blue, and magenta reflects red & blue. Secondary pigments colors then are blue, green, and red because they absorb two primary light colors and reflect their own light color back.

The Electromagnetic Spectrum

The electromagnetic spectrum covers a wide range of wavelengths and photon energies. Visible light ranges from 400 to 700 nanometers. About 550 nanometers, which is a yellowish green, is the wavelength to which our eyes are most responsive. Only a small portion of the electromagnetic spectrum is visible to us. The smaller the wavelength, the more energy each photons of the light has.

Electromagnetic Spectrum (cont.)

Radio waves are very long (a few centimeters to 6 football fields) and can be used to send signals. These signals are transmitted by radio stations. They transmit information and music via amplitude modulation (AM) and frequency modulation (FM).

Wavelengths other that visible light serve useful purposes:

Microwaves (a few millimeters long) are also used in communications. Microwave ovens are great for heating food since food is primarily water, and microwaves have just the right frequency to get water molecules vibrating.Infrared (micrometers in length) are used in remote controls to change the channel, and they are also radiated by objects that are warmer than their surrounding (like your body). They make night vision equipment possible.

Ultraviolet light is harmful to our bodies because its wavelength is so small. Short wavelength mean high energy for photons. UV causes our skin to tan and burn. Fortunately, the ozone layer blocks most UV radiation, but prolonged exposure to the sun should be avoided, since UV rays can cause skin cancer. On the positive side UV radiation helps people to produce their own vitamin D.

Electromagnetic Spectrum (cont.)

X-rays are even more energetic, and hence more dangerous, than UV rays, but luckily they cannot penetrate our ozone layer. They are produced in space and of course are used by doctors to get pictures of your bones.

Gamma rays are the most energetic of the light waves and little is known about them other than they are very harmful to living cells and are used by doctors to kill certain cells and for other operations. They are produced in nuclear explosions. Like other high energy rays, our atmosphere protects us from gamma rays.

Astronomers have many different types of telescopes at their disposal to observe the universe in all parts of electromagnetic spectrum. Some telescopes are ground-based; others are space-based:

Arecibo Spitzer

Hubble Keck

Compton

Parallax and Depth PerceptionParallax is any alteration in the apparent position of an object due to a change in the position of the observer. A simple demonstration of this effect can be seen by extending your thumb at arm’s length. Then close one eye at a time and note how your thumb appears to jump left and right relative to the background. Now move your thumb closer and note how the jump is greater. This technique can be used in astronomy to find a star’s distance from Earth. For distant objects like stars, astronomers must move their “eyes” as far apart as possible. They accomplish this by observing the apparent displacement of a star against the background of more distant stars resulting from the change of the Earth’s position in orbit. The parallax angle is exaggerated in the picture below.

Parallax and Depth Perception (cont.)

Solution on next Solution on next slide.slide.

1o

The picture is not to scale. The diameter of Earth’s orbit is very small compared to the distance of the star being measured, which in turn is very small compared to the distance of the background stars. For this reason the angular displacement of points A and B, as seen from Earth at any point in its orbit, is almost exactly the same as twice the parallax angle.Problem: Back on Earth Schmedrick attempts to figure out how far away a certain nearby star is. He measures a 2 deg. angular separation of distant stars A & B that lined up with a nearer star when observed six months apart. How far away is the star? (Earth is 93 million miles from the sun.)

A

B

Parallax and Depth Perception (cont.)

Answer: Let R be the Earth-sun distance, x the distance to the star in question, and = the angular separation of the distant stars.

Thus, tan ( / 2) = R / x. With = 2 and R = 93 million miles,

x 5.33 109 miles

The Star Schmedrick is looking at is approximately 5 billion miles away. So, Schmed must have been imagining this star, because it’s much too close for any real-life star (other than the sun).

R

2 o

x

Luminous vs. Illuminated

A luminous object is a body that produces its own light such as the sun or a light bulb.

An illuminated object is a body that reflects light, just like the moon, people, and buildings.

Some objects, like water and glass, transmit light to some extent. In order to be seen, light must come from an object one way or the other.

Luminosity & MagnitudeLuminosity is the rate at which energy of all types, and in all directions, is radiated by an object. The luminosity of a star depends on its size and its temperature: L R 2 T 4. The sun is a medium-sized star with a luminosity of 3.8×1026 J/s. The known luminosities of stable stars range from about a millionth that of the sun for a relatively cool white dwarf to about a million times that of the sun for the hottest known super-giant star. Astronomers assign stars magnitudes based on how bright they are. Apparent magnitude measures how bright a star appears to be from Earth. Absolute magnitude measures its true luminosity. The brighter a star appears, the lower its apparent magnitude. Every 5 magnitudes corresponds to brightness changing by a factor of 100. For example, a magnitude 1 star is 10,000 times brighter than a magnitude 11 star. Besides the sun, the brightest star as seen from Earth is Sirius with an apparent magnitude of -1.6.

Light Transmission

Transparent: Materials, such as window glass, through which light can travel easily and through which other objects can clearly be seen.

Translucent: Materials, such as glass blocks, through which light can pass through but no clear image can be seen. Opaque: Materials which absorb and reflect light. Objects cannot be seen through the material. Most objects are opaque.

Thin Films & Thin Film Interference

Guinness Soap Bubble Records

Soap Bubble Soap Bubble WallWall

Continued on Next Continued on Next SlideSlide

incident ray

reflected rays

The thin film effect refers to colors seen in such things as soap bubbles and oil spills. It occurs as a result of the constructive and destructive interference of light waves, not because of refraction as in a prism. When light hits a bubble, some of it is reflected by the outer (air-soap) interface (ray #1), while some penetrates the bubble wall and is reflected by the inner (soap-air) interface (ray #2). The two reflected rays interfere with one another. Typically, most wavelengths will be out of phase since #2 has to travel a greater

#1

#2

distance than #1. However, one wavelength will be in phase and this corresponds to the color produced. The color depends on how great the difference in distance is that the two rays travel, and this distance depends on bubble thickness. The variations in thickness (thinner at the top, thicker at the bottom) are responsible for the different colors.

Thin Films (cont.)

When light moving through the air encounters the denser film the reflected ray is inverted, just like a pulse traveling down a slinky is inverted when it reflects at the connection point with a heavier spring. The transmitted ray is not inverted, which is also the situation with slinky and spring. When the transmitted ray encounters the soap-air interface at the inside of the bubble, again some of it is reflected back. This time, however, the wave is not inverted (just as a pulse traveling on a heavy spring is not inverted when it reflects at the connection point with a slinky). The two reflected rays may or may not be in phase; it depends on how thick the film is.

Since white light is comprised of many wavelengths, those that are nearly in phase after reflecting off the bubble surfaces will be reinforced (constructive interference). This is the color that will appear on the bubble. The other wavelengths are out of phase (destructive interference) and are, at least partially, cancelled out.

Since gravity causes the bubble to be thicker near the bottom, different wavelengths are reinforced at different heights, producing bands of colors. Interestingly, a bubble on the space shuttle will not produce bands of different colors. This is because the shuttle is in free fall around Earth, which means bubbles behavior as if they’re in a gravity-free environment. Thus, bubbles are of uniform thickness. Continued on Next Continued on Next

SlideSlide

Bubble Bubble Wall Wall /4 /4

Original Original WaveWave

InvertedInverted wave wave from 1from 1stst reflection reflection superimposed superimposed with upright with upright wave from 2wave from 2ndnd reflectionreflection

Thin Films (cont.)

air outside air outside bubblebubble

air inside air inside bubblebubble

Transmitted Transmitted wave wave superimposed superimposed with upright with upright wave from 2wave from 2ndnd reflectionreflection

So how do we determine which color will be produced at a particular point on a bubble or other thin film? Well, if the thickness of the film is /4, then light of wavelength will be reinforced. Here’s why: The round trip in the film will be /2. This means the two waves will be in phase, since one was inverted and one wasn’t.

Polarized LightBeam oBeam o’’ LightLight

A polarizing filter is made of a material with long A polarizing filter is made of a material with long molecules that allow electromagnetic waves of one molecules that allow electromagnetic waves of one orientation through. If a wave has an electric field orientation through. If a wave has an electric field with any other orientation, the filter will only allow with any other orientation, the filter will only allow a component to pass through, absorbing the rest. Note a component to pass through, absorbing the rest. Note that only transverse waves such as light can be that only transverse waves such as light can be polarized. Much of the light we see is at least polarized. Much of the light we see is at least partially polarized. For example, when light reflects partially polarized. For example, when light reflects off of surfaces it is partially polarized. Some off of surfaces it is partially polarized. Some sunglasses contain polarizing filters which helps to sunglasses contain polarizing filters which helps to block glare (such as the glare that is noticeable when block glare (such as the glare that is noticeable when looking out over a lake on a sunny day).looking out over a lake on a sunny day).

Electric Electric Field Field OrientatioOrientationsns

Light coming directly from the sun or other sources is unpolarized, meaning the electric and magnetic fields oscillate

Polarized Light Glare Molecular View

in many different planes. Polarized light refers to Polarized light refers to light in which all waves have electric fields oscillating in the same plane. light in which all waves have electric fields oscillating in the same plane. Imagine trying to pass a large piece of sheet metal through the bars of a Imagine trying to pass a large piece of sheet metal through the bars of a jail cell. To do this you would have to orient the sheet vertically (or nearly jail cell. To do this you would have to orient the sheet vertically (or nearly so), otherwise the bars would block the sheet. Here, the bars are so), otherwise the bars would block the sheet. Here, the bars are analogous to a polarizing filter, and the sheet is analogous to the plane analogous to a polarizing filter, and the sheet is analogous to the plane in which the electric field is oscillating.in which the electric field is oscillating.

Continued Continued

Polarized Light (cont.)

Blocking Light

Unpolarized light propagates in all orientations. No particular orientation is preferred. When it passes through a filter that only allows vertical components of electric fields to pass, its intensity is cut in half. This is because, on average, the light is “half horizontal and half vertical” in terms of electric field components. All horizontal components are blocked, making the resulting polarized light half as bright.

Now, imagine that you place another filter that is perpendicular to the direction of the first one, i.e., a filter that only allows the horizontal components of electric fields to pass through. This would completely block the remaining light. Thus, any two perpendicular filters will block all incoming light.

Suppose now that the two filters are offset by some angle . Regardless of the angle, the first filter blocks half the light. If = 0, the second filter has no effect. If = 90, the second filter blocks the other half of the light. In gen-eral, when polarized light with an electric field of amplitude E passes through the second filter, the amplitude will drop to E cos. Furthermore, since the energy a wave carries is proportional to the square of its ampli-tude, the intensity of the light will be the original intensity multiplied by cos2.

Continued on Next Continued on Next SlideSlide

“Twisting” of Light

Light Light

EnterEnterss

Light Light ExitsExits

We know that if = 90 between two filters, then no light will make it past the second one. At other angles light will pass through both, changing the orientation of its electric field each time. So, what if we arranged several polarizing filters so that the angle between any two consecutive filters is less than 90? The answer is that light twists its way through the filters, even if the angles between the filters adds up to 90. With each pass the light is oriented in a new direction, and this new orientation has a component parallel to the orientation of the next filter.

Twisting Light

Quantum Mechanic--BackgroundRecall that a black body is an ideal absorber of all incident radiation. A hot black body is also a perfect emitter--radiation is the result of its temperature, and since none of this is absorbed, it is a perfect emitter of radiation. A black body emits all wavelengths of light but not equally; there is always a wavelength in which the radiation peaks. The hotter the black body, the

smaller the peak wavelength. Objects around you are cool, so their peak is in the infrared. The sun is hot enough to peak in the visible spectrum (all other wavelengths are emitted too but at lower intensities).

In the late 19th century classical physics had predicted something impossible: as the temperature rises, the intensity of the peak radiation approaches infinity (red dashed line). The theory did match experimental data for large wavelengths but failed for small ones. This was known as the “ultraviolet catastrophe.”

Planck’s ConstantIn 1900 Max Planck came up with a revolutionary way to resolve the problem by assuming that energy came in discrete amounts (quanta). This was the beginning of quantum mechanics. Each quantum of light is called a

photon, and its energy is given by E = h f, where f is the frequency of the radiation and h is the constant of proportionality called Plank’s constant. The formula states that higher frequency light has proportionally more energy per photon. Einstein lent credence to Plank’s ideas by explaining the photoelectric effect in a similar manner. Robert Millikan did a series of experiments involving the photoelectric effect and calculated the constant:

h = 6.626 10-34 J s.

Before Planck light was considered to be a wave. Today we know it can be interpreted as either a particle or a wave. As a wave, bright light can be explained as a large amplitude in the electric and magnetic fields. As a particle, bright light would be explained by a large number of photons.

Max Plank

Coherent Light

Lamps, flashlights, etc… all produce light. But this light is released in many directions, and the light is very weak and diffuse. In coherent light the wavelength and frequency of the photons emitted are the same. The amplitude may vary. Such things as lasers and holograms are composed of coherent light.

Incoherent

Coherent

Lasers Laser stands for light amplification by stimulated emission of radiation. A laser is a device that creates and amplifies a narrow, intense beam of coherent, monochromatic (one wavelength) light. Here’s how they work.

There are 2 primary states for an atom, an excited state and a ground state. The ground state is the lowest energy, most stable state. In the excited state electrons are in a higher energy level. In a laser, the atoms or molecules of a crystal (such as ruby) or of a gas, liquid, or other substance are excited in the laser cavity so that more of them are at higher energy levels (excited state) than are at lower energy levels. When an excited electron drops back to a lower energy level, a photon of a particular wavelength is released. This photon stimulates other electrons to emit photons. All these photons are in phase.

Holograms

Reference Reference BeamBeam

ObjectObject

Film Film PlatePlate

MirrorMirror

Light Light wave wave interfereinterferencence

LaserLaser Beam Beam SplitterSplitter

Object Object BeamBeam

As with any type of wave, light waves can interfere with one another. The interference of two or more waves will carry the whole information about all the waves. It is on this basis that holograms work. Holograms make use of lasers and they work in the following fashion: (Explanation on next slide.)Explanation on next slide.)

Beam Beam SpreaderSpreader

Holograms (cont.)

As the laser hits the beam splitter, it is split in two. The object beam heads towards the object of interest, while the reference beam heads toward a mirror. The beams are identical until the object beam shines on the object. There some of the light is absorbed; some is reflected toward the film. After reflecting off the mirror, the reference beam is reunited with the object beam on the film. Because one beam interacted with the object and the other didn’t, the two beams will be out of phase and interfere with one another. This interference pattern is imprinted upon the holographic film plate, creating the holographic image.

This pattern records the intensity distribution of the reflected light just as an ordinary camera does. However, it also records the phase distribution. This means that it contains information about where the waves are in their oscillating cycles as they strike the film. To determine this the object beam must be compared with the reference beam. This is accomplished via the interference. Also unlike an ordinary photo, a hologram contains all its information in every piece of it.

When viewed in coherent light the object appears in 3-D and viewing a hologram from different angles will reveal the object from different angles.

Luminous Flux & IlluminanceLuminous flux, , is the rate at which an object emits visible light (adjusted to the responsiveness of the human eye, which is most sensitive to yellow-green). It is measured in lumens. Imagine a light source in the center of a sphere. Luminous flux is the quantity of light that hits the surface of the sphere per unit time. The size of the sphere is irrelevant. If the sphere were larger, the same quantity of light would reach the surface every second, so the flux wouldn’t change. However, this light would be more spread out, so the illuminance of the surface would be less than it was with the same candle in the smaller sphere. Also called illumination, the symbol forilluminance is E, not to be confused with energy, and is defined as luminous flux per unit of surface area: E = / S. The SI unit for illuminance is the lux, which is a lumen per square meter. The illuminance of the sun is about 100,000 lx (lux); for the full moon it’s about 0.2 lx. A common, non-SI unit for illuminance is the foot-candle, which is equivalent to about 10.8 lx.

Illuminance vs. Distance

11/4

1/91/16

P 1 m 2 m 3 m 4 m

A point source at P radiates light in all A point source at P radiates light in all directions. The pic below shows how light spreads directions. The pic below shows how light spreads out as it radiates. If the illuminance on the sheet out as it radiates. If the illuminance on the sheet 11 m from P is 1 unit, then m from P is 1 unit, then the illuminance on the sheet 2the illuminance on the sheet 2 m m from P is four times less. This is because doubling the distance from P is four times less. This is because doubling the distance increases the area by a factor of four over which the light is spread. increases the area by a factor of four over which the light is spread. Similarly, Similarly, 33 m from P the illuminance is nine times less, and 4m from P the illuminance is nine times less, and 4 m from P itm from P it’’s 16 s 16 times less. Note the flux (amount of light) is not changing, but the times less. Note the flux (amount of light) is not changing, but the illuminance is because the same amount is spread over different illuminance is because the same amount is spread over different areas. In general, areas. In general, E E is proportional to is proportional to and inversely proportional to the square of the distance. This is reminiscent of Newton’s inverse square law for gravitation.

Solid AnglesWe can measure ordinary, “flat” angles by the ratio of arc length of a circle to the radius of the circle. Imagine two radii shooting out from the center, subtending part of the circumference. By definition this ratio is the measure of the angle between the radii in radians. There are 2 radians in a circle since C = 2 r.

Now imagine a sphere instead of a circle and a cone shooting out from the center rather than a two radii (the apex of the cone is at the center). Instead of part of a circum-ference, the cone subtends part of the surface area of the sphere. A solid angle (measured in steradians) is defined as the ratio of the subtended surface area of the of sphere to the square of its radius. This definition applies even if the subtended area is not circular. There are 4 steradians in a sphere since S = 4 r 2.

angle = 1 radian

radius = 1 unit

arc length = 1 unit

Luminous IntensityRecall that illuminance is flux per unit area. A related quantity is luminous

intensity, I, which is defined as flux per unit of solid angle. Thus, I = Ø / 4 , since there are 4 steradians in a sphere. You can think of luminous intensity as the amount of light contained within a cone whose apex is at the source. The same amount of light confined to a skinnier cone would mean a greater intensity. Just as the “flat” angle is independent of the size of the circle, the solid angle is independent of the size of the sphere. The intensity is the same

at every sheet in the pic below. In a sphere 7 m in radius, I is the flux that falls on a 49 m2 surface on the sphere. The SI unit for intensity is the candela, cd. 1 cd = 1 lumen per steradian. A footcandle is the illuminance one foot away from a 1 candela source.

P 1 m 2 m 3 m 4 m

Efficiency of light sources

Light sources, like light bulbs, vary in efficiency. This means that some bulbs, e.g. fluorescent bulbs, will produce more light while using less energy. (They can do this by producing less waste heat.) The efficiency of a simple machine is the work done by the machine divided by the work put into it. In this context, efficiency (more technically, efficacy) is the rate at which light is produced by the bulb divided by the rate at which

energy is used to produce that light: eff = Ø / P, where P is power. Note that both flux and power are rates, so eff is really “light over energy.” It is measured in lumens per watt. A typical candle has an efficiency of about 0.1 lumen / W. Incandescent bulbs are about 15 lumen / W, but a fluorescent bulb is closer to 70 lumen / W. A monochromatic source emitting light of around 555 nm in wavelength would be the ideal in terms of efficiency, with all of its radiation being visible to us instead of infrared (waste heat).

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